Optimal. Leaf size=80 \[ -\frac{91125 x^7}{56}-\frac{443475 x^6}{32}-\frac{229149 x^5}{4}-\frac{19986237 x^4}{128}-\frac{41793093 x^3}{128}-\frac{306103815 x^2}{512}-\frac{308539921 x}{256}-\frac{616195041}{1024 (1-2 x)}+\frac{156590819}{2048 (1-2 x)^2}-\frac{33674025}{32} \log (1-2 x) \]
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Rubi [A] time = 0.0454977, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{91125 x^7}{56}-\frac{443475 x^6}{32}-\frac{229149 x^5}{4}-\frac{19986237 x^4}{128}-\frac{41793093 x^3}{128}-\frac{306103815 x^2}{512}-\frac{308539921 x}{256}-\frac{616195041}{1024 (1-2 x)}+\frac{156590819}{2048 (1-2 x)^2}-\frac{33674025}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{308539921}{256}-\frac{306103815 x}{256}-\frac{125379279 x^2}{128}-\frac{19986237 x^3}{32}-\frac{1145745 x^4}{4}-\frac{1330425 x^5}{16}-\frac{91125 x^6}{8}-\frac{156590819}{512 (-1+2 x)^3}-\frac{616195041}{512 (-1+2 x)^2}-\frac{33674025}{16 (-1+2 x)}\right ) \, dx\\ &=\frac{156590819}{2048 (1-2 x)^2}-\frac{616195041}{1024 (1-2 x)}-\frac{308539921 x}{256}-\frac{306103815 x^2}{512}-\frac{41793093 x^3}{128}-\frac{19986237 x^4}{128}-\frac{229149 x^5}{4}-\frac{443475 x^6}{32}-\frac{91125 x^7}{56}-\frac{33674025}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0244228, size = 71, normalized size = 0.89 \[ -\frac{23328000 x^9+175348800 x^8+628425216 x^7+1466857728 x^6+2647685376 x^5+4449695040 x^4+9877535360 x^3-26671311588 x^2+11541996324 x+3771490800 (1-2 x)^2 \log (1-2 x)-1001301969}{3584 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 61, normalized size = 0.8 \begin{align*} -{\frac{91125\,{x}^{7}}{56}}-{\frac{443475\,{x}^{6}}{32}}-{\frac{229149\,{x}^{5}}{4}}-{\frac{19986237\,{x}^{4}}{128}}-{\frac{41793093\,{x}^{3}}{128}}-{\frac{306103815\,{x}^{2}}{512}}-{\frac{308539921\,x}{256}}-{\frac{33674025\,\ln \left ( 2\,x-1 \right ) }{32}}+{\frac{156590819}{2048\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{616195041}{2048\,x-1024}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06547, size = 82, normalized size = 1.02 \begin{align*} -\frac{91125}{56} \, x^{7} - \frac{443475}{32} \, x^{6} - \frac{229149}{4} \, x^{5} - \frac{19986237}{128} \, x^{4} - \frac{41793093}{128} \, x^{3} - \frac{306103815}{512} \, x^{2} - \frac{308539921}{256} \, x + \frac{2033647 \,{\left (1212 \, x - 529\right )}}{2048 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{33674025}{32} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46915, size = 319, normalized size = 3.99 \begin{align*} -\frac{93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 24774428 \, x + 7530594841}{14336 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.140008, size = 70, normalized size = 0.88 \begin{align*} - \frac{91125 x^{7}}{56} - \frac{443475 x^{6}}{32} - \frac{229149 x^{5}}{4} - \frac{19986237 x^{4}}{128} - \frac{41793093 x^{3}}{128} - \frac{306103815 x^{2}}{512} - \frac{308539921 x}{256} + \frac{2464780164 x - 1075799263}{8192 x^{2} - 8192 x + 2048} - \frac{33674025 \log{\left (2 x - 1 \right )}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.32742, size = 77, normalized size = 0.96 \begin{align*} -\frac{91125}{56} \, x^{7} - \frac{443475}{32} \, x^{6} - \frac{229149}{4} \, x^{5} - \frac{19986237}{128} \, x^{4} - \frac{41793093}{128} \, x^{3} - \frac{306103815}{512} \, x^{2} - \frac{308539921}{256} \, x + \frac{2033647 \,{\left (1212 \, x - 529\right )}}{2048 \,{\left (2 \, x - 1\right )}^{2}} - \frac{33674025}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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